Other thread subtopics:

Covariate Models Using Weight (Allometric Scaling)

Covariate Models Using CrCL

Predefined Models vs. "Context-Sensitive" Emperical Models

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From: "Piotrovskij, Vladimir [JanBe]" <VPIOTROV@janbe.jnj.com>

Subject:Covariate Models Using Weight

Date: Tue, 16 Nov 1999 11:24:31 +0100

Dear Rebecca,

You should be more specific when posting your questions. The convergence behaviour of NONMEM depends very much on the METHOD you select for $EST. It can be totally different for METHOD=0 (the default first order linearization method) and for METHOD=1 (first-order conditional method). It would be better if you attach the entire NM-TRAN control.

The way you implement the fixed effect of WT is not optimal. Firstly, it is preferable to center it using median WT (say, 70) as offset. Then, it worth to include an intercept in the fixed effect model, e.g.: TVCL=THETA(1)+THETA(2)*(WT-70). THETA(1) corresponds to the typical clearance at median WT. Lastly, I would strongly recommend to avoid using TRANS3. You will have much less troubles with TRANS4.

Hope this helps,

Vladimir

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Vladimir Piotrovsky, Ph.D.

Janssen Research Foundation

Clinical Pharmacokinetics

B-2340 Beerse

Belgium

Email: vpiotrov@janbe.jnj.com

Date: Wed, 17 Nov 1999 14:09:55 +1300

From: Nick Holford <n.holford@auckland.ac.nz>

Subject: Covariate Models Using Weight

I agree with your comments about the value of centering to improve the estimation of parameters in the covariance model. There is no need to be obsessional about using the median. Any convenient value that is approximately in the middle of your data is fine. Remember that the final parameter estimate you obtain will be defined in terms of this centering value. I prefer to refer to this centering value as the standard covariate value e.g. a weight of 70 kg is a widely recognized standard for human adult weight.

However, I have argued (Holford 1996) on data driven and biological grounds that models for body size should be based on the allometric model:

CLi = CLstd * (Wi/Wstd)**3/4

Vi = Vstd * (Wi/Wstd)**1

where CLi, Vi are CL and V in an individual with weight Wi and Wstd is a standard weight e.g. 70 kg. CLstd and Vstd are the population parameters standardized to the size of an individual with weight Wstd.

The exponent value of 3/4 for CL can be justified on theoretical grounds (West et al. 1997) and is supported by allometric studies of a wide variety of body functions with an estimate of this exponent indistinguishable from 0.75 (Peters 1983). Justification for V and other body volumes having an allometric exponent of 1 has been reviewed by Anderson et al. 1997.

Note these models do not have an intercept parameter. I believe it is an a priori more reasonable model to expect that CL or V will be zero when WT is zero. I prefer to put my faith in biology and mechanism when choosing a model. I resort to statistical heuristics (e.g. change in log-likelihood) when the biology or mechanism is not obvious.

I suspect that empirical estimates of allometric exponents reported in the literature for PK parameters are most likely indistinguishable from the a priori value of 3/4 for CL and 1 for V. If the null hypothesis that the exponents are 3/4 and 1 is rejected then careful thought should be given to other confounding factors in the data rather than rejecting a priori well established biological principles.

Anderson BJ, McKee D, Holford NHG. Size, myths and the clinical pharmacokinetics of analgesia in paediatric patients. Clinical Pharmacokinetics 1997;33:313-327

Holford NHG. A size standard for pharmacokinetics. Clin. Pharmacokin. 1996: 30:329-332

Peters RH. The ecological implications of body size. Cambridge University Press.1983

West GB. Brown JH. Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science. 1997; 276:122-6

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm

From: Rebecca Wrishko <wrishko@unixg.ubc.ca>

Subject: Covariate Models Using Weight

Date: Wed, 17 Nov 1999 11:54:08 -0800

Further to the discussion and suggestions forwarded by Vladimir Piotrovskij and Nick Holford with respect to implementation of a parameter centered by some median/mean weight, does the distribution of the population weights have to be fairly narrow, that is is a narrow range, to use TVCL=Theta(1)+Theta(2)*(wt-70)? I attempted to implement this suggestion for a small (6) pediatric population with a mean weight of 20kg (11.2, 17, 18.7, 22.2, 25, 33) with an ADVAN3 TRANS3 subroutine under default (Method 0) estimation and was unable to obtain a successful execution due to a negative V value. However, if the mean weight was changed to 12 and the NM-TRAN control stream (below) was executed final parameter estimates were obtained. Does the centering for mean weight strategy require a robust population? Also I believe that the estimates of theta(1)-1.09L/hr, theta(3)-4.09L, theta(5)-3.17L are in the units of /12kg . However, when one wishes to translate to TVCL (with units of /kg) must the theta(1) and theta(2) values be added and then divided by weight given in the parenthetical term or mean weight (ie. 1.09+0.145/12 or 1.09+0.145/20)?

$SUBROUTINES ADVAN3 TRANS3; Two Compartment Linear Model of entire

population

$PK

TVCL=THETA(1)+THETA(2)*(WT-12) ; typical clearance normalized for wt

CL=TVCL*(1+ETA(1)) ; mean clearance

TVV=THETA(3)+THETA(4)*(WT-12) ; typical central volume normalized for wt

V=TVV*(1+ETA(2)) ; mean central volume

TVVSS=V+THETA(5)+THETA(6)*(WT-12) ; typical vss normalized for wt

VSS=TVVSS*(1+ETA(3)) ; mean theta 3

Q=THETA(7)

K=CL/V; reparameterization lines

K12=Q/V

K21=Q/(VSS-V)

S1=V

$THETA (0,0.5)

(0,0.01)

(0,0.5)

(0,0.01)

(0,1)

(0,0.01)

(0,3)

$OMEGA .25 .25 .25 ; fifty percent cv

$SIGMA .04 ; twenty percent cv

$ERROR

Y=F*(1+EPS(1)) ; proportional error term

$ESTIMATION MAXEVAL=850 SIGDIGITS=4

$COVARIANCE

Thank you for your assistance

Rebecca

>Rebecca Wrishko

>Division of Clinical Pharmacy

>Faculty of Pharmaceutical Sciences

>University of British Columbia

>Vancouver, British Columbia, Canada

>Email: wrishko@unixg.ubc.ca

Date: Mon, 22 Nov 1999 17:01:29 -0800 (PST)

From: ABoeckmann <alison@c255.ucsf.edu>

Subject: centering

Rebecca Wrishko <wrishko@unixg.ubc.ca> sent the following question:

> does the distribution of the population weights

> have to be fairly narrow, that is is a narrow range, to use

> TVCL=Theta(1)+Theta(2)*(wt-70)? I attempted to implement this suggestion

> for a small (6) pediatric population with a mean weight of 20kg (11.2, 17,

> 18.7, 22.2, 25, 33) with an ADVAN3 TRANS3 subroutine under default (Method

> 0) estimation and was unable to obtain a successful execution due to a

> negative V value. However, if the mean weight was changed to 12 and the

> NM-TRAN control stream (below) was executed final parameter estimates were

> obtained.

Sounds like she had trouble with

TVV=THETA(3)+THETA(4)*(WT-20)

I suggest that she add the NOABORT option to the Estimation record:

$ESTIMATION MAXEVAL=850 SIGDIGITS=4 NOABORT

Explanation:

Early in the Estimation Step, NONMEM makes rather large changes in thetas. If it makes theta 3 relatively small, and theta 4 relatively large, then for some subjects having WT<20 it may happen that TVV<0. There is no reasonable way to tell NONMEM to bound the thetas so that this cannot happen. Instead, we tell NONMEM to use "PRED error recovery". NONMEM will avoid thetas that give rise to the error condition (THETA recovery)

It is not wise to rely on the NOABORT option if the error messages in PRDERR file persist well into the Estimation Step, because this indicates that the true minimum may lie close to a region in theta space that NONMEM is prevented from visiting. But if the error message appears only once, early in the Estimation Step, NOABORT is a legitimate way of bounding a function of thetas.

She says that when "WT-12" was used, no set of thetas that NONMEM tried gave rise to negative TVV, but the problem is that V was not truly centered. Similar remarks apply to the model for CL.

For more information, see Users Guide Part IV, IV. G (p. 51-52). Note that the "EXIT" statement is effectively coming from PREDPP rather than from her own code, but the effect of NOABORT is the same.

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Other thread subtopics:

Covariate Models Using Weight (Allometric Scaling)

Covariate Models Using CrCL

Predefined Models vs. "Context-Sensitive" Emperical Models